Headhunters: First Round Interviews which questions to ask

Hi,

I was wondering, if you are having a screening interview with a HH for an position at a PE Shop, what kind of questions do you ask? Asking in depth questions about investments or their strategy does not make much sense, as they dont know it. Same applies for everything related to team culture etc. On the other hand, it would make little sense to ask questions you can research on your own.

So what kind of questions do you ask? I want to sound interested in the role without the thread of asking stupid questions (e.g. questions they cant answer or questions i can research on my own).

Thanks